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Uniqueness and parameter dependence of positive solutions of third order boundary value problems with $p$-laplacian

Pages: 515 - 522, Issue Special, September 2011

 Abstract        Full Text (322.5K)              

John R. Graef - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)
Lingju Kong - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)

Abstract: We consider the boundary value problem with nonhomogeneous three-point boundary condition Sufficient conditions are obtained for the existence and uniqueness of a positive solution. The dependence of the solution on the parameter $\lambda$ is also studied. This work extends and improves some recent results in the literature on the above problem, especially those in the paper [L. Kong, D. Piao, and L. Wang, Positive solutions for third order boundary value problems with $p$-Laplacian, Result. Math. 55 (2009) 111{128].

Keywords:  Positive solutions, boundary value problems, uniqueness, dependence on a parameter
Mathematics Subject Classification:  Primary: 34B15; Secondary: 34B10, 34B18

Received: June 2010;      Revised: April 2011;      Published: October 2011.